Inverse Problems in Population Balances. Determination of Aggregation Kernel by Weighted Residuals

The phenomenology of particulate systems are embedded into the population balance model through breakage, aggregation, or growth kernels. Aggregation kernel is a difficult kernel to predict from first principle because of its nonlinear nature. In this work we demonstrate a new methodology to obtain the aggregation kernel through inverse problem approach. This new approach is based on the method of weighted residuals and does not rely on specific traits of the system like self-similarity. The residual approach reduces the inverse problem into solution of a set of linear equations. However, the system of equations is badly conditioned and therefore requires regularization for accurate solution. In this work Tikhonov regularization technique has been used. The new method has been demonstrated successfully for constant, sum, and product kernel.